If a set of weights, ..., is associated to the dataset, ...,, the weighted harmonic mean is defined by

It is also equivalent to any weighted harmonic mean where all weights are equal.

( If neither is the case, then a weighted harmonic mean or weighted arithmetic mean is needed.

The term weighted average usually refers to a weighted arithmetic mean, but weighted versions of other means can also be calculated, such as the weighted geometric mean and the weighted harmonic mean.

The solution can also be written as a weighted harmonic mean of the initial condition and the carrying capacity,

The boxer design provides good vibration mitigation due to the principles of a balanced engine because the movement of each piston is largely countered by a piston in the opposing cylinder bank, eliminating the need for a counter-rotating weighted crankshaft ( harmonic balancer ), but with some vibration from offsets.

The arithmetic, harmonic, geometric, generalised, Heronian and quadratic means are all Chisini means, as are their weighted variants.

Another example of a weighted mean is the weighted harmonic mean.

This should not be confused with statistical objects such as the weighted mean, the weighted geometric mean or the weighted harmonic mean, since no such formulas are used upon imposing Cauchy boundary conditions.

* Trimean – the weighted arithmetic mean of the median and two quartiles.

In probability theory, the expected value ( or expectation, or mathematical expectation, or mean, or the first moment ) of a random variable is the weighted average of all possible values that this random variable can take on.

Non-investable indices are indicative in nature, and aim to represent the performance of some database of hedge funds using some measure such as mean, median or weighted mean from a hedge fund database.

For a probability distribution, the mean is equal to the sum or integral over every possible value weighted by the probability of that value.

The average molecular mass is the abundance weighted mean ( average ) of the molecular masses in a sample.

It can produce a weighted mean that has less variability than the arithmetic mean of a simple random sample of the population.

The weighted mean is similar to an arithmetic mean ( the most common type of average ), where instead of each of the data points contributing equally to the final average, some data points contribute more than others.

The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics.

If all the weights are equal, then the weighted mean is the same as the arithmetic mean.

As Broadway itself becomes increasingly weighted down by trite, heavy-handed, commercially successful musicals and inspirational problem dramas, the American theatre is going through an inexorable renaissance in that nebulous area known as `` off-Broadway ''.

A long book heavily weighted with military technicalities, in this edition it is neither so long nor so technical as it was originally.

TAI as a time scale is a weighted average of the time kept by over 200 atomic clocks in over 50 national laboratories worldwide.

The candela ( or ; symbol: cd ) is the SI base unit of luminous intensity ; that is, power emitted by a light source in a particular direction, weighted by the luminosity function ( a standardized model of the sensitivity of the human eye to different wavelengths, also known as the luminous efficiency function ).

The relative atomic mass ( historically and commonly also called " atomic weight ") of an element is the average of the atomic masses of all the chemical element's isotopes as found in a particular environment, weighted by isotopic abundance, relative to the atomic mass unit ( u ).

An additional method of long-term ocean-based sequestration is to gather crop residue such as corn stalks or excess hay into large weighted bales of biomass and deposit it in the alluvial fan areas of the deep ocean basin.

The formula used to calculate the final scores is a weighted sum of the votes.

According to the U. S. National Historic Landmark nomination for the arch, it is a " weighted catenary " instead.

However where there can be a difference weighted in favour of females is where the injury results in permanent scarring to the skin.

A loaded, weighted or crooked die is one that has been tampered with to land with a specific side facing upwards more often than it normally would.

The total is then weighted by and multiplied by the DD.

Linear filters satisfy the superposition condition, i. e. if an input is a weighted linear combination of different signals, the output is an equally weighted linear combination of the corresponding output signals.

The output of the filter is formed as the weighted sum of those delayed signals, as is depicted in the accompanying signal flow diagram.

* Friction — Sensitivity is expressed in terms of what occurs when a weighted pendulum scrapes across the material ( it may snap, crackle, ignite, and / or explode ).

A digraph with weighted edges in the context of graph theory is called a network.

Only in this appropriately weighted case does the H measure the effective amount of light falling on the film, such that the characteristic curve will be correct independent of the spectrum of the light.

If one thinks of L as some generalised type of weighted average, taken to the limit, a tauberian theorem allows one to discard the weighting, under the correct hypotheses.

Scores are computed based on number of correct answers, with weighted values ; harder problems and test cases are given more weight than easier ones.

With multiple segment metering ( also known as matrix metering ), the values of the different segments are combined and weighted to set the correct exposure.

* Traditional Present Value Approach-in this approach a single set of estimated cash flows and a single interest rate ( commensurate with the risk, typically a weighted average of cost components ) will be used to estimate the fair value.

In the Bayesian approach to this problem, instead of choosing a single parameter vector, the probability of a given label for a new instance is computed by integrating over all possible values of, weighted according to the posterior probability:

Using this phylogenetic framework, we inferred the genus ' historical biogeography by using weighted ancestral-area analysis and dispersal-vicariance analysis in combination with a Bayesian relaxed molecular-clock approach and paleogeographical data.

The essential purpose of NEPA is to ensure that environmental factors are weighted equally when compared to other factors in the decision making process undertaken by federal agencies. The act establishes the national environmental policy, including a multidisciplinary approach to considering environmental effects in federal government agency decision making.

The above equation of weighted averages always applies, but the following approach may be more easily visualized.

Some PHAs use a " lottery " approach, where there can be as many as 100, 000 applicants for 10, 000 spots on the waitlist, with spots being awarded on the basis of weighted or non-weighted lotteries, with priority sometimes given to local residents, the disabled, veterans, and the elderly.

Using weighted least squares regression and a sliding window approach they show that as time passes, words, both in terms of tokens ( in text ) and types ( in vocabulary ), have become longer.

The weighted average cost of capital is an approach to determining a discount rate.